1. Field of the Invention
The present invention relates to a non-invasive measurement of a temperature distribution within a target body, which utilizes a nuclear magnetic resonance (NMR) imaging technique.
2. Description of the Background Art
In recent years, a need for developing a method for measuring a temperature distribution within a target body such as a living body non-invasively has been felt strongly in a wide range of medical fields including temperature measurement, tissue temperature measurement, and hyperthermia treatment.
This need is motivated by the fact that the temperature within the living body is a physical quantity which reflects many physiological functions of the living body, so that the information on the temperature distribution can be useful in diagnosing diseases such as circulation malfunction and tumors, as well as in monitoring the temperature change during the heating process used in hyperthermia treatment.
To this end, there has been several propositions to utilize the temperature dependent parameters of the NMR signals, such as a thermal equilibrium magnetization, longitudinal relaxation time, transverse relaxation time, and diffusion constant, for the purpose of the non-invasive measurement of the temperature distribution within a target body, which include the following representative cases.
(1) M.sub.0 : Thermal equilibrium magnetization
The thermal equilibrium magnetization M.sub.0 is known to be inversely proportional to the temperature, as expressed by the following expression (1). EQU M.sub.0 =N.sub.0 (T).gamma..sup.2 hB.sub.0 /4kT (1)
where T is an absolute temperature, N.sub.0 is a proton density, .gamma. is a gyromagnetic ratio, h is a Planck constant, k is a Boltzmann constant, and B.sub.0 is a static magnetic field strength.
According to this expression (1), the temperature gradient of the thermal equilibrium magnetization M.sub.0 for the proton system in pure water is -0.36%/K at the temperature of 40.degree. C., so that the temperature can be estimated from the change of the thermal equilibrium magnetization M.sub.0.
However, the temperature gradient of the thermal equilibrium magnetization M.sub.0 takes a very small value, and the measurement must be made on a basis of the proton density image obtained by the NMR imaging, so that the very high precision measurement is required in order to achieve the sufficient temperature resolution and accuracy.
(2) T.sub.1 : Longitudinal relaxation time
When the speed of the molecular motion is quantified by a time constant .tau..sub.C of a correlation function concerning positions of protons, the longitudinal relaxation time T.sub.1 can be approximately expressed by the following expressions (2) and (3). EQU T.sub.1 .varies..omega..sub.0.sup.2 .eta.(T)/T for .omega..sub.0 .tau..sub.C &gt;&gt;1 (2) EQU T.sub.1 .varies.T/.eta.(T) for .omega..sub.0 .tau..sub.C &lt;&lt;1 (3)
where .omega..sub.0 is a Larmor angular frequency and .eta. is a viscosity coefficient of the proton system.
Here, the temperature gradient is 2.2%/K for the proton system in pure water at the temperature of 40.degree. C., which is larger than the temperature gradient of the thermal equilibrium magnetization M.sub.0. Thus, the longitudinal relaxation time T.sub.1 is a thermally more sensitive parameter than the thermal equilibrium magnetization M.sub.0.
However, the use of this longitudinal relaxation time T.sub.1 for the temperature measurement has been associated with the following problems.
First, it is necessary to measure the temperature dependency of each tissue in advance, because the ratio of the free water and the bound water and the difference of the viscosity affect the temperature dependency.
Secondly, in order to measure this longitudinal relaxation time T.sub.1 at a precision of few %, it becomes necessary to pay a great amount of attention to the stability in the operation of the measurement system as a whole.
Thirdly, the measurement of the longitudinal relaxation time is quite time consuming.
(3) T.sub.2 : Transverse relaxation time
The transverse relaxation time can be expressed as a function of temperature, as in the following expressions (4) and (5). EQU T.sub.2 .varies.T/.eta.(T) for .omega..sub.0 .tau..sub.C &gt;&gt;1 (4) EQU T.sub.2 =T.sub.1 .varies.T/.eta.(T) for .omega..sub.0 .tau..sub.C &lt;&lt;1 (5)
where .omega..sub.0 is a Larmor angular frequency and .eta. is a viscosity coefficient of the proton system.
However, the use of this transverse relaxation time T.sub.2 for the temperature measurement has been associated with the following problems.
First, it is necessary to measure the temperature dependency of each tissue in advance, because the ratio of the free water and the bound water and the difference of the viscosity affect the temperature dependency.
Secondly, in order to measure this transverse relaxation time T.sub.2 at a precision of few %, it becomes necessary to pay a great amount of attention to the stability in the operation of the measurement system as a whole.
(4) D: Diffusion constant
The diffusion constant is known to have the temperature dependency expressed by the following expression (6). EQU D.varies.exp(-E/kT) (6)
where E is an activation energy.
According to this expression (6), the temperature change (T-T.sub.0) can be determined from the diffusion constants D.sub.0 and D obtained before and after the temperature change, by the following expression (7). EQU (T-T.sub.0).tbd.(kT.sub.0.sup.2 /E)[(D-D.sub.0)/D.sub.0 ] (7)
However, such a use of this diffusion constant D for the temperature measurement is based on assumptions that (T-T.sub.0)&lt;&lt;T.sub.0 and the activation energy is constant for each tissue, so that there are chances for the errors to be introduced due to the inaccuracy of these assumptions.
Furthermore, in such a conventional non-invasive measurement of the temperature distribution within a target body utilizing the temperature dependent parameters of the NMR signals, there has been a possibility for the measured temperature distribution to be spoiled by the error due to a displacement of the target body during the temperature measurement, especially when the target body is a living body, because the temperature dependency of the chemical shifts is substantially smaller compared with an inhomogeneity of the magnetic field caused by a body movement of the target body.